FIG. 1 illustrates a base station (101) of a cellular communication system covering cell 1 (102) and cell 2 (103), and user equipment (104). A cell is an area of radio coverage of a base station and each base station covers one or more cells by one or more antennas (105), (106). The cell is identified by a cell identity.
In most telecommunication systems, when a user terminal initializes access to the system, it initially determines the time synchronization, including the symbol timing and the frame timing, the frame comprising several symbols. In an example 3GPP cellular system, the symbol timing is obtained from detecting a primary synchronization signal, which is transmitted via the Primary Synchronization Channel P-SCH, whereas the frame timing is determined by decoding a secondary synchronization signal transmitted via the Secondary Synchronization Channel S-SCH. The secondary synchronization signal also typically conveys information about a cell identity or a cell group identity. A cell group identity identifies a group of one or more cells.
In a cellular communication system, such as an Orthogonal Frequency Division Multiplex OFDM system, symbols are transmitted in radio frames. In an example OFDM system, the time interval of the radio frames is 10 ms and the synchronization symbols are placed equidistantly 5 ms apart. Ability to determine frame timing and cell specific information from a single S-SCH symbol may be required. In a further example 3GPP system, two secondary synchronization code SSC sequences are multiplexed in an S-SCH symbol. The SSC sequences are taken from a set of 31 m-sequences and cell-specific scrambling is applied. Indices m0 and m1 of two SSC sequences in an S-SCH symbol can be regarded as representing elements of a codeword of length 2. Each such S-SCH codeword is denoted by [m0,m1].
In an E-UTRA system, a code design is adopted with the following specified code construction to map a cell group ID, NID to codeword elements:
                                          m            0                    =                                    m              ′                        ⁢            mod            ⁢                                                  ⁢            31                          ⁢                                  ⁢                              m            1                    =                                    (                                                m                  0                                +                                  ⌊                                                            m                      ′                                        /                    31                                    ⌋                                +                1                            )                        ⁢            mod            ⁢                                                  ⁢            31                          ⁢                                  ⁢                                            m              ′                        =                                          N                ID                            +                                                q                  ⁡                                      (                                          q                      +                      1                                        )                                                  /                2                                              ,                                          ⁢                      q            =                          ⌊                                                                    N                    ID                                    +                                                                                    q                        ′                                            ⁡                                              (                                                                              q                            ′                                                    +                          1                                                )                                                              /                    2                                                  30                            ⌋                                ,                                    q              ′                        =                          ⌊                                                N                  ID                                /                30                            ⌋                                ,                                    (        0        )                            where 0≦NID≦167.The code construction for encoding group IDs in the prior art generates codewords for 0≦NID≦167, which satisfy m0≦m1.        